Liang Hua
Department of Biostatistics, St. Jude Children's Research Hospital, 332 North Lauderdale St., Memphis, TN 38105-2794.
Comput Stat Data Anal. 2006 Feb 10;50(3):675-687. doi: 10.1016/j.csda.2004.10.007.
Partially linear models with local kernel regression are popular non-parametric techniques. However, bandwidth selection in the models is a puzzling topic that has been addressed in literature with the use of undersmoothing and regular smoothing. In an attempt to address the strategy of bandwidth selection, we review profile-kernel based and backfitting methods for partially linear models, and justify why undersmoothing is necessary for backfitting method and why the "optimal" bandwidth works out for profile-kernel based method. We suggest a general computation strategy for estimating nonparametric functions. We also employ the penalized spline method for partially linear models and conduct intensive simulation experiments to explore the numerical performance of the penalized spline method, profile and backfitting methods. A real example is analyzed with the three methods.
具有局部核回归的部分线性模型是流行的非参数技术。然而，模型中的带宽选择是一个令人困惑的话题，文献中已通过欠平滑和正则平滑来解决。为了探讨带宽选择策略，我们回顾了基于轮廓核和回退拟合的部分线性模型方法，并阐明了为什么欠平滑对回退拟合方法是必要的，以及为什么“最优”带宽适用于基于轮廓核的方法。我们提出了一种估计非参数函数的通用计算策略。我们还将惩罚样条法应用于部分线性模型，并进行了大量模拟实验以探究惩罚样条法、轮廓法和回退拟合方法的数值性能。用这三种方法分析了一个实际例子。
